"We are continuing to clean and re-clean the open stretch of beach and we are confident the amounts of residual oil in the water are low."
But there was still oil in the environment and people needed to be vigilant if they chose to go into the water, he said.
"People should be careful and look out for any sign of oil contamination. Although the residual oil is a lot less toxic than fresh oil, people should still avoid it."
He said sports such as kayaking and boating where there is unlikely to be contact with floating oil was likely to be safe, but people had to keep an eye out for any globules of the potentially toxic substance.
The rest of the beach, from Tay Street to Maketu, remained closed to the public.
Captain van Wijngaarden said for areas west of Mount Maunganui and east of Maketu, people should take care and avoid the water if they suspect it to be contaminated.
"People should continue to avoid direct contact with the oil and if they do smell or see oil in the water, they should leave the area."
He said the clean-up efforts and wildlife recovery operations were continuing, with teams and equipment sent to any reports of oil or oiled wildlife.
MNZ Salvage Unit Manager Bruce Anderson said continuous pumping of oil from Rena had continued overnight and this morning.
"Today the salvage team will be focusing on speeding up the flow rate. We have good weather and will take advantage of it while we can."
By Saturday night, salvors had extracted 256 tonnes of the estimated 1700 tonnes of oil on board the vessel.
A tug boat Go Canopus has been put on standby in Tauranga to act as a back-up vessel for the oil removal operations, reported Radio New Zealand.
The boat will be used if the weather turns too sour for the barge Awanuia, which has been used to hold extracted oil so far.
The back-up tug will be fitted with oil tanks.
Detailed public information is available online at http://www.toiteorapublichealth.govt.nz/rena-public, and people are encouraged to call 0800 OIL SPILL with any sightings of the black substance.